Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Ta có:
\(2^{3^{2^3}}=2^{3^8}=2^{6561}=2^{3.2187}=\left(2^3\right)^{2187}=8^{2187}\)
\(3^{2^{3^2}}=3^{2^9}=3^{512}\)
Vì: 8 > 3 và 2187 > 512
\(\Rightarrow8^{2187}>3^{512}\)
\(\Rightarrow2^{3^{2^3}}>3^{2^{3^2}}\)
Vậy: \(2^{3^{2^3}}>3^{2^{3^2}}\)
\(\left(\frac{1}{3}\right)^{2x-1}-\frac{1}{3^2}=-\frac{2}{27}\)
=> \(\left(\frac{1}{3}\right)^{2x-1}=-\frac{2}{27}+\frac{1}{9}\)
=> \(\left(\frac{1}{3}\right)^{2x-1}=\frac{1}{27}\)
=> \(\left(\frac{1}{3}\right)^{2x-1}=\left(\frac{1}{3}\right)^3\)
=> 2x - 1 = 3
=> 2x = 3 + 1
=> 2x = 4
=> x = 4/2 = 2
\(\Leftrightarrow2^{x+1}.3^y=4^x.3^x\)
\(\Leftrightarrow2^{x+1}.3^y=2^{2x}.3^x\)
\(\Leftrightarrow\frac{3^y}{3^x}=\frac{2^{2x}}{2^{x+1}}\)
\(\Leftrightarrow3^{y-x}=2^{x-1}\)
Nếu \(x>1\Rightarrow\) vế trái lẻ, vế phải chẵn pt vô nghiệm
\(\Rightarrow x=1\Rightarrow3^{y-1}=1\Rightarrow y=1\)
2^6=64
8^2=64. Vậy 2^6=8^2
5^3=125, 3^5=243. Vì 243>125 nên 5^3<3^5
1: \(A=2+2^2+2^3+\cdots+2^{100}\)
=>\(2A=2^2+2^3+2^4+\cdots+2^{101}\)
=>\(2A-A=2^2+2^3+2^4+\cdots+2^{101}-2-2^2-2^3-\cdots-2^{100}\)
=>\(A=2^{101}-2\)
2: \(B=1+5+5^2+5^3+\cdots+5^{150}\)
=>\(5B=5+5^2+5^3+\cdots+5^{151}\)
=>\(5B-B=5+5^2+5^3+\cdots+5^{151}-1-5-5^2-\cdots-5^{150}\)
=>\(4B=5^{151}-1\)
=>\(B=\frac{5^{151}-1}{4}\)
3: \(C=3+3^2+\cdots+3^{1000}\)
=>\(3C=3^2+3^3+\cdots+3^{1001}\)
=>\(3C-C=3^2+3^3+\cdots+3^{1001}-3-3^2-\cdots-3^{1000}\)
=>\(2C=3^{1001}-3\)
=>\(C=\frac{3^{1001}-3}{2}\)
Câu 1:
A = 2 + 2\(^2\) + 2\(^3\) + ... + 2\(^{100}\)
2A = 2\(^2\) + 2\(^3\) + ... + 2\(^{100}\) + 2\(^{101}\)
2A - A = (2\(^2\) + 2\(^3\) + ... + 2\(^{100}\)+ 2\(^{101}\)) -(2 + 2\(^2\) + 2\(^3\) + ... + 2\(^{100}\))
A = 2\(^2\) + 2\(^3\) + ... + 2\(^{100}\)+ 2\(^{101}\) - 2 - 2\(^2\) -2\(^3\) - ... - 2\(^{100}\)
A = (2\(^2\) - 2\(^2\)) + (2\(^3\) - 2\(^3\)) + ... + (2\(^{100}\) - 2\(^{100}\)) + (2\(^{101}\) - 2)
A = 0 + 0 + 0 + ... + 0 + 2\(^{101}\) - 2
A = 2\(^{101}\) - 2
A = 3 + 32 + ...... + 360
A = ( 3 + 32 ) + .....(359 + 360 )
A = ( 3 + 32 ) + ........+ 358 . ( 3 + 32 )
A = 12 + ....... + 358 . 12
A = 12 . ( 1+ ....... + 358 ) : 4 ( đpcm )
Nguyễn Hiền Minh mik la chu nick do ( nhug no bi mat vi quen luu ) nen mik cam on bn :V
A = 1 + 4 + 42 + ... + 499
4A = 4 + 42 + ... + 4100
4A - A = 4100 - 1
3A = 4100 - 1
=> 4100 - 1 + 1 = 4x
=> 4100 = 4x
=> x = 100
Ta có:
\(2^{3^{2^3}}=2^{3^8}=2^{6561}=2^{3.2187}=8^{2187}\)
\(3^{2^{3^2}}=3^{2^9}=3^{512}\)
Ta thấy \(8^{2187}>3^{512}\Rightarrow2^{3^{2^3}}>3^{2^{3^2}}\)
\(2^{3^{2^3}}=2^{3^8}=2^{6561}\)
\(3^{2^{3^2}}=3^{2^9}=3^{512}\)
Tới đây mk chịu để mk suy nghĩ đã!